-
Ground State neutron Spectroscopic Factors for Z=3-24
isotopes
Jenny Lee, M.B. Tsang, and W. G. Lynch
National Superconducting Cyclotron Laboratory and Department of
Physics and Astronomy, Michigan State University, East Lansing, MI
48824
Abstract
Past measurements of the angular distributions for (d,p) and
(p,d) reactions on
targets with Z=3-24 leading to the ground states have been
analyzed systematically using
the theory of Johnson-Soper adiabatic approximation and
Distorted-Wave Born-
Approximation, adopting nucleon-nucleus global optical model
potentials as input. In all,
the ground state neutron spectroscopic factors (SF) for 80
nuclei have been obtained. The
consistency of the method is evaluated by comparing
spectroscopic factors obtained
separately in (p,d) and (d,p) reactions. The values also
correlate strongly with Endt’s
compilation when available, but the current method of extracting
spectroscopic factors is
more general and the values obtained are more consistent.
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I. Introduction
The spectroscopic factors describe the overlap between the
initial and final state
in the reaction channels and yield important information about
single-particle orbitals in
many nuclei [1-5]. Single nucleon transfer reactions such as
(d,p) or (p,d) reactions have
been used extensively to extract the spectroscopic information
of the single nucleon
orbits [1-6]. Specifically, these measurements allow the
extraction of the spectroscopic
factors by taking the ratios of the experimental cross-sections
to the predicted cross-
sections from a reaction model. The most common model used is
the Distorted Wave
Born Approximation (DWBA) theory [3-5]. For (p,d) and (d,p)
transfer reactions
involving deuteron, the effects from deuteron break up can be
significant at high energy
and the correction is generally taken into account using the
Johnson-Soper adiabatic
approximation [7].
Some of the difficulties in the past extractions of
spectroscopic factors have been
associated with different parameterizations used in the reaction
models, different
normalizations, and different assumptions used in the analysis
[8, 9]. It is not unusual to
find spectroscopic factors for a particular nucleus that
fluctuate by factors of 2-3.
Recently, it has been shown that systematic and consistent
analysis of the angular
distributions for the 12C(d,p)13C and 13C(p,d)12C reactions
yield the ground state
spectroscopic factors to within 15% over a range of equivalent
deuteron incident energy
from 12 to 60 MeV [9]. There is an abundant amount of transfer
reaction data collected in
the past 40 years. These data, if analyzed in a consistent
manner, may provide a
systematic view of the spectroscopic factors over the nuclear
chart and may shed insight
as to how to extract the spectroscopic information about the
valence orbitals for unstable
nuclei far from the valley of beta stability [10-12].
II. Reaction model
In the present work, we follow the algorithm developed in ref.
[9] and use a
modified version of the code TWOFNR [13] to perform the transfer
reaction model
calculations using the same input parameters labeled as CH in
ref. [9]. The transfer
cross-sections are calculated within the Johnson-Soper (JS)
adiabatic approximation [7]
to the neutron, proton, and target three-body system using the
phenomenological nucleon
nucleus optical model potentials [14]. This calculation includes
the effects of breakup of
-
the deuteron in the field of the target. The valence neutron
binding potential is Woods-
Saxon in shape with fixed a radius parameter of 1.25 fm and a
diffuseness parameter of
0.65 fm [9]. The depth of the potential is normalized to the
experimental binding energy.
All calculations make the local energy approximation (LEA) for
finite range effects [15]
using the Zero-range strength (Do2=150006.25 fm3) and range
(β=0.7457 fm) parameters
of the Reid soft-core 3S1-3D1 neutron-proton interaction [16].
Nonlocality corrections
with range parameters of 0.85 fm and 0.54 fm are included in the
proton and deuteron
channels, respectively [17]. The same set of input parameters is
used throughout in the
present work to extract the spectroscopic factors [18].
III Compilation and digitization of angular distribution
data
For the present work, we mainly focus on the transfer reactions
A(d,p)B and its
inverse reaction B(p,d)A where the nucleus A is considered to be
composed of the core B
plus the valence neutron n. Table 1 contains 423 reactions that
we have examined. For
clarity, we include shorthand literature references [19-239] in
the table.
Nearly all the angular distributions listed in Table 1 have been
digitized from the
published figures. The few exceptions are those found in the
Nuclear Science References
(NSR) database of the National Nuclear Data Center (NNDC) [240].
The data from NSR
are in tabulated form and the sources of these data came from
the Former Soviet Union or
Japan whose journals are not widely available in the United
States. These non-US and
non-European data complement our search in the Physical Review
Journals, Nuclear
Physics and occasionally in Physics Letters. While we make an
effort to search out nearly
all the relevant experiments that published the absolute
differential cross-sections, we
may have missed some reactions especially if the incident energy
is below 10 MeV and
above 70 MeV. Except when noted, the table does not include
reactions with cross-
sections published in arbitrary units. The data and calculations
will be posted in a website
[241]. Eventually, we hope all the digitized data used in this
work will be adopted by the
NSR.
By checking some of the data carefully and sometimes repeating
the digitization
several times, we estimate the uncertainties introduced by the
digitization process to be
less than 10%. For illustration, we use the data for the
reaction 14N(d,p)15N at Ed=12 MeV
[21, 82]. This set of data was first published in tabulated form
in ref [21]. The tabulated
-
data are plotted as closed points in Figure 1. Later the authors
in ref. [82] plotted the data
in a figure. We digitized the data in [82] and compare our
digitized data (open points)
with the tabulated data (closed points) in Figure 1. We see a
difference of less than 10%
between the two sets of data. Of course, the digitization errors
also depend on the actual
size of the graphs available in the original literature. As
described later, generally, errors
introduced by digitization are small compared to the
uncertainties in the absolute cross-
section measurements.
IV. Extraction of spectroscopic factors
For nearly all the nuclei we study, we use the ground state l
values determined
from the angular distributions and the jπ values of the valence
neutron ground states
found in the isotope tables [242]. In general, the experimental
angular distributions at the
backward angle are more sensitive to the effects of inelastic
couplings and other higher-
order effects and are not well reproduced by most reaction
models. Furthermore,
discrepancies between the shapes from calculations and
experiment are much worse in
the valley. Thus, we follow the procedures developed in ref. [9]
and others that the
spectroscopic factor is extracted by fitting the reaction model
predictions to the angular
distribution data at the first peak, with emphasis on the
maximum. The accuracy in
absolute cross-section measurements near the peak is most
important. When possible, we
take the mean of as many points near the maximum as we can to
extract the spectroscopic
factors. We will use the angular distributions of 14N(d,p)15N
shown in Fig 1 to illustrate
the procedure we adopt to extract the spectroscopic factors.
In Figure 1, the first 3 data points with θcm
-
as shown in Figure 2, we found that fitting the shoulder gives
more consistent results.
This observation is probably related to the fact that due to
quantum tunneling, the very
forward angle data cannot be described well by classical
calculations [243].
In general, the agreement of the shape of the angular
distributions of the first peak
or shoulder to reaction calculations gives some indication to
the quality of the data. The
numbers of data points in the fit region, which can be described
well by the predicted
angular distributions are included as statistical weights in
Table 1 when the mean
spectroscopic factors for an isotope are computed.
V. Evaluation of the angular distribution measurements
Even though most papers state the uncertainties of their
cross-section
measurements to be 10-20%, the actual disagreements between
experiments are often
larger than the quoted uncertainties. An example is illustrated
in the reactions 11B(d,p)12B
reactions. From the conventional literature, we found two
measurements at deuteron
incident energy of 11.8 MeV [45] and 12 MeV [21]. Since the
incident deuteron energy is
nearly the same, one would expect the angular distributions
plotted in Figure 3 to be the
same within experimental error. Ref. [21] stated that the
accuracy of the absolute cross-
section measurements is 15% while ref. [45] quoted an error of
6%, which is smaller than
the closed symbols in Fig 3. Not only do the cross-sections
differ sometimes by a factor
of two, the shapes of the distributions (especially the first
peak) are not even the same. In
this case, the shape of the angular distributions in ref. [45]
agrees with the calculations
better than that measured in ref. [21]. Fortunately for this
reaction, we were able to find
another measurement in the NNDC database [46]. This latter
angular distribution agrees
with ref. [45]. Data in ref. [45] was measured nearly 40 years
later than data in ref. [21].
Naively, one might expect newer measurements to be better as
beam quality and
detection systems tend to improve with time. However, when
another reaction, 12C(d,p)13C at Ed=11.8 MeV from ref. [45] (closed
circles) is compared to three other
published angular distributions at Ed=11.8 MeV (closed diamonds)
[30], 12 MeV (open
circles) [21], 12 MeV (open diamonds) [59], the cross-sections
in the first peak measured
in ref. [45] is consistently low. No uncertainties in the
measurements are given in ref.
[30] and ref. [59] but it is clear that data in ref. [45] do not
agree with other
measurements.
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Cross comparisons of angular distributions sometimes help to
establish common
systematic problems when one set of measurements was performed
by the same group
with the same set up. An example is illustrated in the
40Ca(d,p)41Ca reactions in ref. [181]
where the ground state angular distributions of 41Ca at Ed=7, 8,
9, 10, 11 and 12 MeV
have been measured. Figure 5 shows the extracted spectroscopic
factors as a function of
incident deuteron energy for all the 40Ca(d,p)41Ca reactions.
For clarity in presentation,
no uncertainties are plotted. The extracted spectroscopic
factors from ref. [181] (open
circles) are consistently larger than the spectroscopic factors
extracted from different
experiments with the same reactions at the same energy. Detailed
comparisons of the
angular distribution data show essentially the same effect, that
the differential cross-
sections measured in ref. [181] are systematically higher than
the other measurements.
Clearly, there must be some problems in the determination of the
absolute cross-sections
in ref. [181]. Since it is not possible to find the cause after
so many years. In our review
of the data, we ignore spectroscopic factor values determined
from ref. [181].
Similarly we include the weight of only one spectroscopic factor
at 11 MeV
determined using the data in ref. [29] for the 9Be(d,p)10Be
reaction as most of the data in
ref. [29] are low when compared to the available data from other
measurements. To also
include data from Ed=10 and 10.5 MeV for the reaction
9Be(d,p)10Be will increase the
weights of these measurements in the mean values. All the SF
values not used are listed
in Column 5. In general, a brief comment follows in the last
column of Table I if the data
set is considered to be problematic.
The disagreements between data sets suggest that it is not
reliable to use the
quoted uncertainties by the experimenters. Rather, we have found
that the most important
aspect of quality control of the data is to have as many
independent measurements as
possible. Comparisons of different measurements help to weed out
bad ones. The large
number of measurements compiled in Table I provide some
assurance of the quality of
the spectroscopic factors extracted in the present work.
VI. Transfer reactions at high and low energy
When Q-value and the transverse and angular momentum transferred
are not well-
matched as in the transfer reactions induced by very low or high
(> 50 MeV) beam
energy, the shape comparisons are also poor. Figure 6 shows the
angular distributions of
-
the protons emitted from the 40Ca(d,p)41Ca (g.s) reaction from
Ed=7.2 to 56 MeV. Only
one angular distribution is presented for each energy. The
agreement between data and
prediction for the first peak improves with increasing energy.
At very low incident or
excitation energy, the comparisons are bad. This phenomenon is
also seen in other
reactions. The spectroscopic factors as a function of incident
energy are shown in Figure
5. The increase of spectroscopic factors observed at Ed
-
dominate. In examining data over a wide range of d or p incident
energy, we find that the
optimum beam energy to study transfer reactions lies between
10-20 MeV per nucleon.
VII. Nuclei with small spectroscopic factors
For the 50Cr(p,d)49Cr reactions, there are two measurements at
beam energy of
17.5 and 55 MeV [223, 224]. In each case, the predicted and
measured angular
distributions are different as shown in Figure 10. From the
magnitude of the measured
cross-sections, a spectroscopic factor value of 0.11 is derived.
The extracted
spectroscopic factor is very low especially for an even-even
nucleus. It is reasonable to
speculate that there is considerable configuration mixing of the
valance nucleus. When
very low SF values (compared to values predicted by the
Independent Particle Model [3-
5]) are obtained, data quality is generally poor and the
predicted shape of the angular
distributions may not agree well with that of the data. Other
examples are 20F, 21Ne, 22Ne, 24Mg, 35Cl, 45Sc, 48Ti, 50Cr, 51Cr,
and 51V nuclei.
In the case of 46Ti(d,p)47Ti reactions [214, 215], both
measurements at Ed=7 and
10 MeV are very different from the predicted cross-sections and
disagree with each other
in shape and absolute cross-sections. We did not extract
spectroscopic factors for the
nucleus of 47Ti.
VIII. Comparison of Spectroscopic factors obtained from (p,d)
and (d,p) reactions
The neutron pickup (d,p) and neutron stripping (p,d) reactions
are inverse reactions,
both of which connect the ground states of the target and
projectile nuclei. They should
yield the same values of the spectroscopic factors. From Table
I, we select the nuclei,
which have been studied reasonably well by both neutron pick-up
and stripping reactions
from and to the ground state. The averaged SF values are listed
in the 2nd and 4th column
of Table II. The numbers of measurements contributing to the
averages are listed right
next to the mean values in the 3rd and 5th columns.
There are strong correlations between the spectroscopic factors
determined from the
(p,d) and (d,p) reactions as shown in Figure 8. The solid line
indicates perfect agreement.
As these are independent measurements determined from similar
procedure outlined
above, the scatter of the data points could be used to determine
the error bars. Assuming
the uncertainties of each of the measurement are the same, x%.
By requiring the chi-
square per degree of freedom to be unity, x can be determined
and in this case x=20%.
-
The obtained uncertainty of 20% is consistent with analysis with
large number of
measurements such as 12C(d,p)13C and 40Ca(d,p)41Ca. Examinations
of large number of
measurements in Table I suggest that the uncertainties in the
extraction of the
spectroscopic factors are largely limited by the agreement
between measurements.
In Table II, we have excluded measurements for 7Li, 34S and 10Be
nuclei due to
large uncertainties associated with either the associated (p,d)
or (d,p) measurements.
Including these 3 measurements increase x to 30%.
Finally, we can compute the spectroscopic factor values and the
associated
uncertainties. The SF values are obtained from the weighted
average of independent
measurements from both the (p,d) and (d,p) reactions listed in
Table 1 from which the
low energy (
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X. 14C(d,p)15C reactions
The 14C(d,p)15C reaction is interesting because 15C has a
loosely bound halo
neutron. It is an important reaction to provide good
cross-comparisons between the
spectroscopic factors obtained from one-nucleon knock-out and
transfer reactions [245].
In addition, this reaction is a good candidate to extract
spectroscopic factors using the
combined asymptotic normalization coefficient (ANC) method
[246].
For the 14C(d,p)15C reaction, there are three references [71, 74
and 75] with Ed>10
MeV. When data from these references are plotted in Figure 8,
the data do not agree with
each other within a factor of two. However, in each case, the
spectroscopic factors quoted
in the original references are within 20% of each other (0.88
[74], 1.03 [71], 0.99 [75]).
The near agreement of the published SF values, even though the
measured cross-sections
are very different, illustrates the problem when spectroscopic
factors of desired values
could be obtained by choosing different input parameters in the
analysis. It underscores
the importance of analysis with a systematic and consistent
approach as studied here.
Since data with first peak or forward angle peak missing are
generally not used in
our analysis, we exclude ref. [71, 75]. The predicted angular
distribution shape (curve)
shows good agreement with ref. [74] with data less than 15° and
we choose to adopt the
extracted SF from this data set. The value of 1.1 is about 35%
higher compared with the
SF’s values extracted at low energy.
XI. Dependence of spectroscopic factors on neutron separation
energy
Recent measurements of spectroscopic factors from single-nucleon
“knock-out”
reactions with radioactive and stable nuclei show increasing
quenching of the
spectroscopic factor values with respect to large basis shell
model predicted values with
nucleon separation energy [247, 248]. The wide range of isotopes
studied in this work
includes nuclei with neutron-separation energies ranging from
0.5 to 19 MeV as listed in
Table III. To examine any quenching trend, we compute the
neutron spectroscopic factors
using Oxbash, a large basis shell model code [249, 250]. The
interactions used in the
calculations are listed in Table 3. Due to the amount of CPU
times involved, we cannot
compute the SF values from Oxbash for every nucleus. As
discussed in detail in ref. [18],
excluding the deformed nuclei and nuclei with small SF values,
most of the extracted
-
spectroscopic factors agree well with the predicted values from
large basis shell model to
20%.
Figure 11 shows the ratio of the experimental SF values to the
LB-SM values
from Oxbash as a function of the neutron separation energy.
Within the experimental
uncertainties, we do not see any systematic quenching of the
spectroscopic factors with
increasing nucleon separation energy as in the nucleon knockout
reactions induced by
radioactive beams. Rather, there seems to be some indication
that the trend is the
opposite, i.e., the SF’s values are smaller than the predicted
values for nuclei with small
neutron separation energy. (This trend persists in a smaller
subset of the nuclei such as
the Ca isotopes plotted as solid stars in Figure 11.)
The structures of the neutron rich nuclei with small neutron
separation energy are
of general interest. For loosely bound nuclei, knockout
reactions with radioactive beams
suggest no quenching. In our data set, there are seven nuclei
with with Sn
-
(d,p) reactions, most extracted values have uncertainties less
than 20%, mainly coming
from experimental measurements. The present compilation of the
neutron ground state
spectroscopic factors of 80 nuclei would provide important
reference points to future
analysis on spectroscopic factors especially for rare nuclei.
They also provide testing
grounds for more sophisticated theoretical work on transfer
reactions and development in
nuclear structure model. At the very least, the simple theory
with minimum assumption
presented in this paper predicts the shape of the first peak of
the angular distributions
quite reliably. Such knowledge is useful in planning future
transfer experiments with
radioactive beams.
Acknowledgement
The authors would like to thank Prof. J. Tostevin for his
generosity in giving us
the TWOFNR code and helping us use it. We would like to thank
Prof. K. Kemper for
many fruitful discussions and encouragement over the past two
years. We would also
like to acknowledge JINA (Joint Institute of Nuclear Physics)
for providing support in
creating the web site that contains the digitized and calculated
angular distributions for
reactions listed in Table 1 [241]. JL acknowledged the support
from the Summer for
Undergraduate Research Experience (SURE) program at the Chinese
University of Hong
Kong. This work was supported by the National Science Foundation
under Grant No.
PHY-01-10253.
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Table I: List of reactions studied in this work. SF stands for
spectroscopic factors. Not all the SF values extracted are used in
computing the averages of the spectroscopic factor for a specific
nucleus. The extracted values not used are listed in the 5th
column. Most of these include reactions at low beam energy
(Ebeam
-
10Be 9Be(d,p)10Be 6.5 J,IZV,64,440,2000 1.51 5 10Be 9Be(d,p)10Be
7 J,IZV,64,440,2000 1.44 4 10Be 9Be(d,p)10Be 7.5 J,IZV,64,440,2000
1.04 2 10Be 9Be(d,p)10Be 8 J,IZV,64,440,2000 1.03 1 10Be
9Be(d,p)10Be 8.5 J,IZV,64,440,2000 1.08 2 10Be 9Be(d,p)10Be 9
J,IZV,64,440,2000 1.07 2 10Be 9Be(d,p)10Be 9.5 J,IZV,64,440,2000
1.00 2 10Be 9Be(d,p)10Be 10 J,IZV,64,440,2000 1.06* 2 10Be
9Be(d,p)10Be 10.5 J,IZV,64,440,2000 1.14* 2 10Be 9Be(d,p)10Be 11
J,IZV,64,440,2000 1.13* 2 BD 10Be 9Be(d,p)10Be 11.8 PR164(1967)1274
2.00* 3 BD 10Be 9Be(d,p)10Be 11.8 NPA53(1964)77 1.42 2 10Be
9Be(d,p)10Be 12.5 J,YF,45,312,(1987) 1.65 4 10Be 9Be(d,p)10Be 15
NPA266(1976)29 1.69 4 10Be
9Be(d,p)10Be 15.3 J,YF,64,1995,2001 1.36 1.53 4 10Be
9Be(d,p)10Be 17.3 NPA236(1974)77 0.97* 3 BS 10Be 9Be(d,p)10Be 28
PR126(1962)1059 2.19 * 2 BS 10Be 10Be(p,d)9Be 49.8 Liu, thesis
(2005) 2.87 * 10 BD 11Be 10Be(d,p)11Be 12 NPA157(1970)305 0.43 3
11Be 10Be(d,p)11Be 25 NPA315(1979)124 0.51 0.476 4 11Be
11Be(p,d)10Be 35.3 NPA683(2001)48 0.56 0.56 2 10B 10B(p,d)9B 33.6
PR167(1968)963 0.55 3 10B 10B(p,d)9B 49.5 NPA141(1970)158 0.42
0.485 3 11B 10B(d,p)11B 4.5 NPA147(1970)65 1.08 2 11B 10B(d,p)11B
4.75 NPA147(1970)65 1.03 3 11B 10B(d,p)11B 5 NPA147(1970)65 0.82 2
11B 10B(d,p)11B 5.25 NPA147(1970)65 0.82 2 11B 10B(d,p)11B 5.5
NPA147(1970)65 0.77 2 11B 10B(d,p)11B 8.2 PR131(1963)304 0.06 AU
11B 10B(d,p)11B 10.1 NP38(1962)114 0.96* 4 BD 11B 10B(d,p)11B 12
PR164(1967)1274 1.21 4 11B 10B(d,p)11B 13.5 NP73(1965)473 1.60 5
11B 10B(d,p)11B 15.5 PR131(1963)304 1.51* 4 11B 10B(d,p)11B 21.5
PR131(1963)304 1.53* 9 11B 10B(d,p)11B 28 PR126(1962)1059 1.48
1.436 2 11B 10B(d,p)11B 28 PR131(1963)304 1.50* 11B 11B(p,d)10B 19
PR129(1963)272 3.06* 3 BD 11B 11B(p,d)10B 33.6 PR167(1968)963 1.25
1.25 3 11B 11B(p,d)10B 45 Liu, thesis (2005) 1.02* 2 BD 12B
11B(d,p)12B 11.8 PRC64(2001)034312 0.43 5 12B
11B(d,p)12B 12 J,NUK,19,693,1974 0.47 0.445 3 12B 11B(d,p)12B 12
PR164(1967)1274 0.42* 1 BS 12C 12C(p,d)11C 19.3 PR128(1962)1810
QV
-
12C 12C(p,d)11C 19.5 PR128(1962)1810 QV 12C 12C(p,d)11C 20
PR128(1962)1810 QV 12C 12C(p,d)11C 30.3 NPA99(1967)669 2.58 3 12C
12C(p,d)11C 39.8 PR132(1963)813 5.28* 4 No 12C 12C(p,d)11C 61
PRC21(1980)2162 3.20 6 12C 12C(p,d)11C 65 NPA255(1975)187 2.94 2.98
3 12C 12C(p,d)11C 65 NPA343(1980)234 2.56* 1 BS 13C 12C(d,p)13C 4
NP82(1966)161 0.63 3 13C 12C(d,p)13C 4.5 NP82(1966)161 0.66 2 13C
12C(d,p)13C 4.5 PR101(1956)209 0.48 2 13C 12C(d,p)13C 4.5
NPA129(1969)405 0.42 2 13C 12C(d,p)13C 7.15 JETP12(1960)1 0.86 4
13C 12C(d,p)13C 8.9 NP22(1961)34 0.91 6 13C 12C(d,p)13C 10.2
PR123(1961)619 0.84 3 13C 12C(d,p)13C 11.8 NP53(1964)77 0.82 3 13C
12C(d,p)13C 11.8 PRC64(2001)034312 0.62 2 13C 12C(d,p)13C 12
NPA477(1988)77 0.70 2 13C 12C(d,p)13C 12 PR164(1967)1274 0.86 3 13C
12C(d,p)13C 12.4 PR123(1961)619 0.76 4 13C 12C(d,p)13C 14.7
PR123(1961)619 0.70 3 13C 12C(d,p)13C 14.8 PR100(1955)235 0.75 1
13C 12C(d,p)13C 15 NPA208(1973)77 0.68 4 13C 12C(d,p)13C 16.6 JPSJ
15(1960)550 0.59 4 13C 12C(d,p)13C 19.6 JPSJ 15(1960)550 0.59 2 13C
12C(d,p)13C 25.9 PR136(1964)B1682 0.66 6 13C 12C(d,p)13C 30
NPA448(86)205 0.59 0.704 3 13C 12C(d,p)13C 51 Liu, thesis (2005) BD
13C 12C(d,p)13C 56 NPA419(84)530 0.95* 1 NP 13C 13C(p,d)12C 35
PRC51(1995)2592 0.76 2 13C 13C(p,d)12C 41.3 NPA470(1987)349 0.83 1
13C 13C(p,d)12C 48.3 Liu, thesis (2005) 0.97 5 13C 13C(p,d)12C 55
PLB27(1968)625 0.88 0.895 3 13C 13C(p,d)12C 65 NPA343(1980)234
1.54* 3 NP 14C 13C(d,p)14C 12 PR164(1967)1274 1.88 5 14C
13C(d,p)14C 13 NPA312(1978)1 1.54 1.753 3 14C 13C(d,p)14C 56
NPA419(1984)530 2.25* 2 NP 14C 14C(p,d)13C 14.5 NPA165(1971)19 0.85
4 14C 14C(p,d)13C 18.5 PR129(1963)272 1.81 3 14C 14C(p,d)13C 27
NPA255(1975)243 0.99 4 14C 14C(p,d)13C 35 NPA509(1990)141 1.59
1.296 5 15C 14C(d,p)15C 2 NPA96(1967) 671 1.10 2 15C 14C(d,p)15C
2.6 NPA96(1967) 671 0.66 1 15C 14C(d,p)15C 3 NPA96(1967) 671 0.72
2
-
15C 14C(d,p)15C 3.4 NPA96(1967) 671 0.78 2 15C 14C(d,p)15C 14
PRC12(1975)1730 1.11 1.11 1 15C 14C(d,p)15C 16 NPA579(1994)125
0.57* BS 15C 14C(d,p)15C 17 NPA255(1975)243 0.40* BS 14N
14N(p,d)13N 14.5 NPA165(1971)19 0.66 7 14N 14N(p,d)13N 18.5
PR122(1961)595 0.74 3 14N 14N(p,d)13N 21 NPA322(1979)117 0.58* 2 NP
14N 14N(p,d)13N 30.3 NPA99(1967)540 0.97 0.732 2 14N 14N(p,d)13N 65
NPA255(1975)187 0.46* 2 NP 15N 14N(d,p)15N 10 NPA333(1980)13 BD 15N
14N(d,p)15N 10.03 NPA382(1982)269 1.62 2 15N 14N(d,p)15N 11.65
NPA382(1982)269 NP 15N 14N(d,p)15N 12 PR164(1967)1274 1.10 3 15N
14N(d,p)15N 14.8 PR105(1957)639 1.52 5 15N 14N(d,p)15N 31
NPA275(1977)212 1.13 1.333 4 15N 14N(d,p)15N 52 NPA275(1977)212
1.80* BD 15N 15N(p,d)14N 18.6 PR122(1961)595 1.71 4 15N 15N(p,d)14N
39.8 PR187(1969)1259 1.38 1.413 2 16N 15N(d,p)16N 14.8
PR105(1957)639 0.42 0.42 4 16O 16O(p,d)15O 18.5 PR129(1963)272
1.66* 4 BS 16O 16O(p,d)15O 19 PR129(1963)272 2.53* 5 BS 16O
16O(p,d)15O 20 PR129(1963)272 2.24 4 16O 16O(p,d)15O 21.27
PR187(1969)1246 1.68 6 16O 16O(p,d)15O 25.52 PR187(1969)1246 2.68 5
16O 16O(p,d)15O 30.3 NPA99(1967)669 2.27 3 16O 16O(p,d)15O 31.82
PR187(1969)1246 2.23 4 16O 16O(p,d)15O 38.63 PR187(1969)1246 2.11 4
16O 16O(p,d)15O 39.8 PR132(1963)813 2.47 2 16O 16O(p,d)15O 45.34
PR187(1969)1246 2.59 4 16O 16O(p,d)15O 65 NPA255(1975)187 2.36
2.257 3 16O 16O(p,d)15O 65 NPA343(1980)234 3.07* 3 NP 17O
16O(d,p)17O 1.3 NP82(1966)161 17O 16O(d,p)17O 2.279 NPA114(1968)330
17O 16O(d,p)17O 2.582 NPA114(1968)330 1.45 17O 16O(d,p)17O 2.864
NPA114(1968)330 1.50 17O 16O(d,p)17O 3.155 NPA114(1968)330 1.54 17O
16O(d,p)17O 3.49 PR123(1961)619 2.53 17O 16O(d,p)17O 4
NP82(1966)161 2.36 17O 16O(d,p)17O 4.11 PR123(1961)619 1.86 17O
16O(d,p)17O 6 NPA112(1968)76 1.22 17O 16O(d,p)17O 6.26
NPA134(1969)561 1.37 17O 16O(d,p)17O 7.5 NPA112(1968)76 1.25 17O
16O(d,p)17O 7.85 NPA112(1968)76 1.20
-
17O 16O(d,p)17O 8 NPA172(1971)663 1.31 17O 16O(d,p)17O 8.2
NPA112(1968)76 1.09 17O 16O(d,p)17O 8.55 NPA112(1968)76 0.96 17O
16O(d,p)17O 9 PR123(1961)619 0.95 17O 16O(d,p)17O 9.3
NPA188(1972)164 0.83 17O 16O(d,p)17O 10 NPA112(1968)76 1.02 3 17O
16O(d,p)17O 10.2 PR123(1961)619 0.97 2 17O 16O(d,p)17O 11
NPA112(1968)76 0.93 2 17O 16O(d,p)17O 11.8 NP53(1964)77 0.60* 3 No
17O 16O(d,p)17O 12 NPA97(1967)541 0.44* 4 No 17O 16O(d,p)17O 12.4
PR123(1961)619 0.97 4 17O 16O(d,p)17O 13.3 NPA188(1972)164 0.96 5
17O 16O(d,p)17O 14.8 PR123(1961)619 1.10 4 17O 16O(d,p)17O 15
PR121(1961)820 0.94 10 17O 16O(d,p)17O 19 PR123(1961)619 0.79* 1 BS
17O 16O(d,p)17O 25.4 NPA218(1974)249 0.87 3 17O 16O(d,p)17O 26.3
NP50(1964)479 1.48* 6 17O 16O(d,p)17O 36 NPA218(1974)249 0.86 0.956
4 17O 16O(d,p)17O 63.2 NPA218(1974)249 1.00 3 17O 17O(p,d)16O 8.62
NPA244(1975)77 1.08 3 17O 17O(p,d)16O 9.56 NPA244(1975)77 1.00 0 BS
17O 17O(p,d)16O 10.5 NPA244(1975)77 0.74 4 17O 17O(p,d)16O 11.16
NPA244(1975)77 0.68 2 17O 17O(p,d)16O 11.44 NPA244(1975)77 0.73 4
17O 17O(p,d)16O 31 PLB31(1970)126 0.80 0.737 2 18O 17O(d,p)18O 18
PRC13(1976)55 1.50 1.500 4 18O 18O(p,d)17O 17.6 PR129(1963)272 1.69
4 18O 18O(p,d)17O 18.2 NPA101(1967)241 1.56 1.585 3 18O 18O(p,d)17O
20 PRC10(1974)445 0.77* 2 BS 18O 18O(p,d)17O 24.4 PRC10(1974)445
1.68* 1 BS 18O 18O(p,d)17O 29.8 PRC10(1974)445 1.35* 3 BS 18O
18O(p,d)17O 37.5 PRC10(1974)445 0.92* 1 BS 18O 18O(p,d)17O 43.6
PRC10(1974)445 1.04* 2 BD 19O 18O(d,p)19O 10 NPA331(1979)269 1.00*
1 NP 19O 18O(d,p)19O 14.8 NPA219(1974)429 0.46 4 19O 18O(d,p)19O 15
PR122(1961)150 0.37 0.41 5 19F 19F(p,d)18F 18.5 PR122(1961)595 1.58
4 19F 19F(p,d)18F 19.3 NPA337(1980)107 1.54 1.563 3 20F 19F(d,p)20F
12 PRC10(1974)1292 0.012 0.012 3 20F 19F(d,p)20F 16 PRC6(1972)21
BD
21Ne 20Ne(d,p)21Ne 11 NPA332(1979)125 0.044 2 21Ne 20Ne(d,p)21Ne
16.4 NPA152(1970)317 0.03 0.034 5 21Ne 21Ne(p,d)20Ne 20
NPA150(1970)609 0.03 0.03 8
-
22Ne 21Ne(d,p)22Ne 10.2 NPA150(1970)609 BD 22Ne 22Ne(p,d)21Ne
18.2 NPA95(1967)591 0.25 4 22Ne 22Ne(p,d)21Ne 20 PR184(1969)1094
0.20 0.229 3 23Ne 22Ne(d,p)23Ne 12.1 NPA152(1970)317 0.24 6 23Ne
22Ne(d,p)23Ne 12.1 NPA95(1967)591 0.24 0.24 6 24Na 23Na(d,p)24Na
7.83 NP45(1963)273 0.56 0.56 3 24Mg 24Mg(p,d)23Mg 27.3
PR177(1969)1737 0.38 4 24Mg 24Mg(p,d)23Mg 33.6 PR172(1968)1078
0.39* 2 BS 24Mg 24Mg(p,d)23Mg 49.2 PRC33(1986)22 0.42 0.40 3 25Mg
24Mg(d,p)25Mg 5 NP88(1966)654 0.74 6 25Mg 24Mg(d,p)25Mg 6
NP88(1966)654 0.49 3 25Mg 24Mg(d,p)25Mg 10 NPA203(1973)177 0.27 3
25Mg 24Mg(d,p)25Mg 12 NPA249(1975)205 0.33 3 25Mg 24Mg(d,p)25Mg 14
PRC10(1974)556 0.27 3 25Mg 24Mg(d,p)25Mg 15 PRC10(1974)556 0.27
0.288 1 25Mg 24Mg(d,p)25Mg 56 NPA419(530)530 0.41* 6 NP 26Mg
25Mg(d,p)26Mg 8 NP88(1966)513 2.99 9 26Mg 25Mg(d,p)26Mg 12
PRC29(1984)2013 1.95 8 26Mg 25Mg(d,p)26Mg 13 NPA430(1984)234 2.54
2.512 7 26Mg 26Mg(p,d)25Mg 20 NPA172(1971)99 1.95 3 26Mg
26Mg(p,d)25Mg 23.95 NPA351(1981)77 3.26 6 26Mg 26Mg(p,d)25Mg 35
PRC38(1988)2026 4.16 3.066 2 27Mg 26Mg(d,p)27Mg 5.07
PR136(1964)B1703 0.83 1 27Mg 26Mg(d,p)27Mg 12 NPA230(1974)317 0.44
0.44 2 27Al 27Al(p,d)26Al 20 NPA204(1973)609 1.45 3 27Al
27Al(p,d)26Al 35 NPA263(1976)293 1.28 1.353 4 28Al 27Al(d,p)28Al 6
NPA197(1972)97 0.42 3 28Al 27Al(d,p)28Al 12 NPA173(1971)414 0.58 3
28Al 27Al(d,p)28Al 23 PRC5(1972)1313 0.83 0.643 1 28Si
28Si(p,d)27Si 27.6 NPA107(1968)659 14.9* 6 28Si 28Si(p,d)27Si 33.6
PR172(1968)1078 4.23 4.23 4 29Si 28Si(d,p)29Si 5 NPA120(1968)94
0.89 1 29Si 28Si(d,p)29Si 5.8 NPA149(1970)605 0.40 2 29Si
28Si(d,p)29Si 9 NPA172(1971)663 0.27 2 29Si 28Si(d,p)29Si 10
NPA189(1972)305 0.55 2 29Si 28Si(d,p)29Si 17.85 NPA408(1983)221
0.35 2 29Si 28Si(d,p)29Si 18 PRC4(1971)1778 0.23 0.367 1 29Si
29Si(p,d)28Si 27.3 PRC2(1970)1440 1.30* 1.30 2 NP 30Si
29Si(d,p)30Si 10 NPA211(1973)7 1.19* 1 BS 30Si 29Si(d,p)30Si 12.3
NPA468(1987)357 NP 30Si 29Si(d,p)30Si 16 NPA202(1973)497 0.62 0.62
1 30Si 30Si(p,d)29Si 27 NPA241(1975)285 0.82 0.82 3 30Si
30Si(p,d)29Si 27.3 PRC2(1970)1440 0.79* 0 NP
-
31Si 30Si(d,p)31Si 7 NPA108(1968)49 0.57 6 31Si 30Si(d,p)31Si 10
NPA108(1968)49 0.57 8 31Si 30Si(d,p)31Si 12.3 NPA468(1987)357 0.69
0.594 2 31Si 30Si(d,p)31Si 12.3 NPA662(2000)112 0.46* 13 32P
31P(d,p)32P 10 NPA210(1973)29 0.63 5 32P 31P(d,p)32P 20
NPA501(1989)413 0.45 0.532 6 32S 32S(p,d)31S 24.5 NPA177(1971)205
3.00* 1 NP 32S 32S(p,d)31S 33.6 PR172(1968)1078 1.46 1.46 NP 33S
32S(d,p)33S 18 PRC4(1971)1778 0.67 0.67 4 34S 33S(d,p)34S 12
NPA173(1971)456 1.82 4 34S 33S(d,p)34S 12 NPA198(1972)209 1.2 1.554
3 34S 34S(p,d)33S 24.5 NPA177(1971)205 1.05 1.05 3 34S 34S(p,d)33S
35 PRC11(1975)654 3.21* 8 BS 35S 34S(d,p)35S 10 NPA170(1971)607
0.29 0.29 5 35S 34S(d,p)35S 11.8 NPA287(1977)94 0.30* 4 BD 37S
36S(d,p)37S 12.3 NPA414(1984)219 0.87 4 37S 36S(d,p)37S 25
PRC30(1984)1442 0.89 0.88 4 35Cl 35Cl(p,d)34Cl 40 NPA189(1972)513
0.33 0.33 4 36Cl 35Cl(d,p)36Cl 7 NPA169(1971)513 0.45 4 36Cl
35Cl(d,p)36Cl 12.3 NPA481(1988)269 0.69 0.69 3 37Cl 37Cl(p,d)36Cl
19 NPA204(1973)609 30* AU 37Cl 37Cl(p,d)36Cl 35 NPA239(1975)189
1.54 3 37Cl 37Cl(p,d)36Cl 40 NPA189(1972)513 0.65 1.031 4 38Cl
37Cl(d,p)38Cl 7.5 NP83(1966)80 1.00 3 38Cl 37Cl(d,p)38Cl 12
NPA225(1974)93 1.74 1.74 5 36Ar 36Ar(p,d)35Ar 27.5 NPA108(1968)113
4.17 5 36Ar 36Ar(p,d)35Ar 33.6 PR172(1968)1078 2.44 3.226 6 37Ar
36Ar(d,p)37Ar 9.162 PRC3(1970)2314 0.28 6 37Ar 36Ar(d,p)37Ar 10.02
PRC10(1974)1050 0.34 5 37Ar 36Ar(d,p)37Ar 18 PRC4(1971)1778 0.36
0.351 6 38Ar 38Ar(p,d)37Ar 26 NPA250(1975)309 2.43 2.43 6 39Ar
38Ar(d,p)39Ar 10.064 PRC5(1972)1278 0.85 3 39Ar 38Ar(d,p)39Ar 11.6
NPA114(1968)392 0.75 0.793 4 40Ar 40Ar(p,d)39Ar 27.5
NPA108(1968)113 1.05 1.05 5 40Ar 40Ar(p,d)39Ar 35 PRC16(1977)1357
2.23* 4 BS 41Ar 40Ar(d,p)41Ar 11.6 NPA114(1968)392 0.60 3 41Ar
40Ar(d,p)41Ar 14.83 NPA250(1975)45 0.53 0.551 7 39K 39K(p,d)38K 35
PRC10(1974)2184 2.10* 4 BS 40K 39K(d,p)40K 12 NPA225(1974)93 1.66
1.66 5 41K 41K(p,d)40K 15 NPA213(1973)317 0.95 0.95 5 42K
41K(d,p)42K 10 NPA311(1978)61 0.86 1 42K 41K(d,p)42K 12
NPA127(1969)343 0.67 0.765 1
40Ca 40Ca(p,d)39Ca 27.3 PL14(1965)113 3.39 3
-
40Ca 40Ca(p,d)39Ca 30 NPA50(1964)49 4.30 1 40Ca 40Ca(p,d)39Ca
33.6 PR172(1968)1078 5.30 3 40Ca 40Ca(p,d)39Ca 40 NPA185(1972)465
4.50 3 40Ca 40Ca(p,d)39Ca 65 PRC48(1993)95 4.15 4.298 6 40Ca
40Ca(p,d)39Ca 65 NPA343(1980)234 4.80* 3 NP 41Ca 40Ca(d,p)41Ca 4.13
NP61(1965)209 41Ca 40Ca(d,p)41Ca 4.69 NP61(1965)209 1.18 41Ca
40Ca(d,p)41Ca 5 NPA109(1968)218 41Ca 40Ca(d,p)41Ca 5
NPA172(1971)652 1.37 41Ca 40Ca(d,p)41Ca 6 NPA109(1968)218 1.30 41Ca
40Ca(d,p)41Ca 6 PRC14(1976)2082 1.22 41Ca 40Ca(d,p)41Ca 7
NPA120(1968)401 1.22 3 41Ca 40Ca(d,p)41Ca 7 PR136(1964)B971 1.20
41Ca 40Ca(d,p)41Ca 7.2 NPA120(1968)401 1.24 3 41Ca 40Ca(d,p)41Ca 8
PR136(1964)B971 1.13 3 41Ca 40Ca(d,p)41Ca 9 NPA172(1971)652 1.01 5
41Ca 40Ca(d,p)41Ca 9 PR136(1964)B971 1.17 3 41Ca 40Ca(d,p)41Ca 10
NPA120(1968)421 0.94 3 41Ca 40Ca(d,p)41Ca 10 NPA225(1974)267 0.92 1
41Ca 40Ca(d,p)41Ca 10 PR136(1964)B971 1.13* BD 41Ca 40Ca(d,p)41Ca
11 NP64(1965)241 1.00 3 41Ca 40Ca(d,p)41Ca 11 NPA140(1970)577 NP
41Ca 40Ca(d,p)41Ca 11 NPA172(1971)652 0.96 6 41Ca 40Ca(d,p)41Ca 11
NPA302(1978)12 1.06 4 41Ca 40Ca(d,p)41Ca 11 PR136(1964)B971 1.26* 3
BD 41Ca 40Ca(d,p)41Ca 11 PR181(1969)1529 0.95 5 41Ca 40Ca(d,p)41Ca
11 PRC14(1976)946 1.00 2 41Ca 40Ca(d,p)41Ca 11.8 NP53(1964)77 0.97
6 41Ca 40Ca(d,p)41Ca 12 NPA140(1970)577 0.96 2 41Ca 40Ca(d,p)41Ca
12 NPA243(1975)100 1.02 6 41Ca 40Ca(d,p)41Ca 12 PR136(1964)B971
1.18* 10 41Ca 40Ca(d,p)41Ca 12.8 PR146(1966)799 1.05 4 41Ca
40Ca(d,p)41Ca 14.3 PR138(1965)B1425 0.98 5 41Ca 40Ca(d,p)41Ca 20
NPA506(1990)159 1.03 0.994 7 41Ca 40Ca(d,p)41Ca 56 NPA419(1984)530
0.74* 4 NP 41Ca 40Ca(d,p)41Ca 56 PRC50(1994)263 1.04* 3 BS 42Ca
41Ca(d,p)42Ca 11 NPA302(1978)12 1.87 3 42Ca 41Ca(d,p)42Ca 12
NPA243(1975)100 1.72 5 42Ca 41Ca(d,p)42Ca 12 PLB40(1972)641 1.76
1.772 3 42Ca 42Ca(p,d)41Ca 26.5 NPA113(1968)303 2.11 4 42Ca
42Ca(p,d)41Ca 40 NPA185(1972)465 2.20 2.14 2 43Ca 42Ca(d,p)43Ca 7
NPA120(1968)401 0.83 3 43Ca 42Ca(d,p)43Ca 7.2 NPA120(1968)401 0.91
3
-
43Ca 42Ca(d,p)43Ca 7.2 PR146(1966)734 0.74 3 43Ca 42Ca(d,p)43Ca
10 NPA120(1968)421 0.64 1 43Ca 42Ca(d,p)43Ca 10 NPA225(1974)267
0.58 0.61 1 43Ca 43Ca(p,d)42Ca 40 PRC7(1973)637 0.64 0.64 4 44Ca
43Ca(d,p)44Ca 8.5 PR155(1967)1229 5.00 5 44Ca 44Ca(p,d)43Ca 17.5
PR144(1966)941 2.77 2 44Ca 44Ca(p,d)43Ca 26.5 NPA113(1968)303 5.17
4 44Ca 44Ca(p,d)43Ca 40 NPA185(1972)465 3.07 3.779 5 45Ca
44Ca(d,p)45Ca 7 NPA120(1968)401 0.54 3 45Ca 44Ca(d,p)45Ca 7
PR156(1967)1255 0.60 2 45Ca 44Ca(d,p)45Ca 7.2 NPA120(1968)401 0.53
2 45Ca 44Ca(d,p)45Ca 10 NPA120(1968)421 0.39 3 45Ca 44Ca(d,p)45Ca
10 NPA225(1974)267 0.39 0.39 3 47Ca 46Ca(d,p)47Ca 7 NPA120(1968)401
0.34 3 47Ca 46Ca(d,p)47Ca 7.2 NPA120(1968)401 0.32 1 47Ca
46Ca(d,p)47Ca 10 NPA120(1968)421 0.25 2 47Ca 46Ca(d,p)47Ca 10
PR138(1965)B1097 0.25 0.25 4 48Ca 48Ca(p,d)47Ca 17.5 PR144(1966)941
8.66 5 48Ca 48Ca(p,d)47Ca 18 PR170(1968)1003 5.33 6 48Ca
48Ca(p,d)47Ca 40 NPA185(1972)465 7.42 7.047 6 49Ca 48Ca(d,p)49Ca
4.5 NPA160(1971)289 1.83 4 49Ca 48Ca(d,p)49Ca 5 NPA160(1971)289
1.79 3 49Ca 48Ca(d,p)49Ca 5.5 NPA160(1971)289 1.66 3 49Ca
48Ca(d,p)49Ca 7 NPA120(1968)401 0.80 3 49Ca 48Ca(d,p)49Ca 7
NPA160(1971)289 0.82 4 49Ca 48Ca(d,p)49Ca 7 PR135(1964)B865 1.48 4
49Ca 48Ca(d,p)49Ca 7.2 NPA120(1968)401 0.86 3 49Ca 48Ca(d,p)49Ca 10
NPA120(1968)421 0.77* 1 NP 49Ca 48Ca(d,p)49Ca 10 NPA225(1974)267
0.62 2 49Ca 48Ca(d,p)49Ca 11.9 NPA303(1978)121 0.59* 2 NP 49Ca
48Ca(d,p)49Ca 13 PRC12(1975)827 0.74 4 49Ca 48Ca(d,p)49Ca 16
PRC12(1975)827 0.67 4 49Ca 48Ca(d,p)49Ca 19.3 PRC12(1975)827 0.66
0.682 3 49Ca 48Ca(d,p)49Ca 56 NPA576(1994)123 0.64* 3 BS 45Sc
45Sc(p,d)44Sc 17.5 PR134(1964)B378 0.29 0.29 3 46Sc 45Sc(d,p)46Sc 7
PR151(1966)939. 0.38 2 46Sc 45Sc(d,p)46Sc 12 PRC46(1992)144 0.49
0.49 2 46Ti 46Ti(p,d)45Ti 17.5 PR135(1964)B389 2.53 3 46Ti
46Ti(p,d)45Ti 26 NPA111(1968)449 2.26 2.376 4 46Ti 46Ti(p,d)45Ti
34.78 NPA152(1970)609 1.25* 3 47Ti 46Ti(d,p)47Ti 7 NP73(1965)321
0.03 47Ti 46Ti(d,p)47Ti 10 NPA196(1972)225 0.01* BD 48Ti
47Ti(d,p)48Ti 13.6 J,YF,25,16,77 0.13 0.13 BS
-
48Ti 48Ti(p,d)47Ti 24.8 NPA152(1970)609 0.12* 4 BD 48Ti
48Ti(p,d)47Ti 29.82 NPA152(1970)609 0.12* 3 BD 48Ti 48Ti(p,d)47Ti
35.15 NPA152(1970)609 0.11 3 48Ti 48Ti(p,d)47Ti 39.97
NPA152(1970)609 0.11 3 48Ti 48Ti(p,d)47Ti 45.05 NPA152(1970)609
0.097 0.106 3 49Ti 48Ti(d,p)49Ti 6 PR159(1967)920 0.29 4 49Ti
48Ti(d,p)49Ti 21.4 PR131(1963)811 0.23 0.23 4 49Ti 49Ti(p,d)48Ti
17.5 PR135(1964)B389 0.23 4 49Ti 49Ti(p,d)48Ti 20.9 NPA177(1971)205
0.26 0.24 4 50Ti 49Ti(d,p)50Ti 13.6 J,YF,25,16,77 6.30 4 50Ti
49Ti(d,p)50Ti 21.4 PR131(1963)811 7.96 7.356 7 50Ti 50Ti(p,d)49Ti
17.5 PR135(1964)B389 5.80 1 50Ti 50Ti(p,d)49Ti 45.05
NPA152(1970)609 5.04 5.149 6 51Ti 50Ti(d,p)51Ti 6 PR136(1964)B438
1.33 51Ti 50Ti(d,p)51Ti 21.4 PR131(1963)811 1.21 1.21 5 51V
50V(d,p)51V 7.5 NPA94(1967)673 1.61 1.61 4 51V 51V(p,d)50V 18.5
PR134(1964)B752 1.30 3 51V 51V(p,d)50V 51.9 PLB73(1978)145 0.72
1.309 2
50Cr 50Cr(p,d)49Cr 17.5 PR160(1967)997 0.11* 5 BS 50Cr
50Cr(p,d)49Cr 55 NPA435(1985)7 0.11 0.11 3 BS 51Cr 50Cr(d,p)51Cr
6.6 NP51(1964)161 0.61 2 51Cr 50Cr(d,p)51Cr 7.5 PR170(1968)1013
0.65 2 51Cr 50Cr(d,p)51Cr 10 NPA198(1972)237 0.25 2 51Cr
50Cr(d,p)51Cr 12 NPA282(1977)87 0.29 0.27 3 52Cr 52Cr(p,d)51Cr 17.5
PR160(1967)997 6.30 6 52Cr 52Cr(p,d)51Cr 18.5 PR134(1964)B752 5.70
6.027 5 53Cr 52Cr(d,p)53Cr 5.41 NP84(1966)398 0.66 3 53Cr
52Cr(d,p)53Cr 5.72 NP84(1966)398 0.56 4 53Cr 52Cr(d,p)53Cr 6
NPA277(1977)374 0.56 4 53Cr 52Cr(d,p)53Cr 6.02 NP84(1966)398 0.65 2
53Cr 52Cr(d,p)53Cr 6.33 NP84(1966)398 0.49 3 53Cr 52Cr(d,p)53Cr 7.5
NPA121(1968)1 0.53 3 53Cr 52Cr(d,p)53Cr 9.14 NP86(1966)65 0.35 3
53Cr 52Cr(d,p)53Cr 10 NPA196(1972)225 0.42 3 53Cr 52Cr(d,p)53Cr 10
NPA206(1973)225 0.42 3 53Cr 52Cr(d,p)53Cr 10 NPA277(1977)119 0.38 1
53Cr 52Cr(d,p)53Cr 10 NP72(1965)273 0.35 0 53Cr 52Cr(d,p)53Cr 10.15
NP86(1966)65 0.36 3 53Cr 52Cr(d,p)53Cr 11.18 NP86(1966)65 0.36 4
53Cr 52Cr(d,p)53Cr 12 NPA167(1971)289 0.41 4 53Cr 52Cr(d,p)53Cr 22
NPA573(1994)1 0.35 0.388 2 53Cr 53Cr(p,d)52Cr 16.6 NPA177(1971)205
0.37 0.37 2 55Cr 54Cr(d,p)55Cr 8 NPA142(1970)469 0.62 2
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55Cr 54Cr(d,p(55Cr 10 NPA337(1980)389 1.07* 2 NP 55Cr
54Cr(d,p)55Cr 10 NPA72(1965)273 0.86 0.86 3
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Table II List of nuclei with spectroscopic factors obtained from
both (p,d) and (d,p) reactions. N_pd and N_dp denote the number of
(p,d) and (d,p) independent measurements included in the
analysis.
A A(p,d)B N_pd B(d,p)A N_dp 11B 1.25 1 1.44 3
11Be 0.56 1 0.46 2 13C 0.83 4 0.71 13 14C 1.3 4 1.75 2
42Ca 2.14 2 1.77 3 43Ca 0.64 1 0.62 2 44Ca 4.16 3 5 1 53Cr 0.37
1 0.39 8 26Mg 3.07 3 2.51 3 15N 1.41 2 1.33 4
21Ne 0.03 1 0.03 2 17O 0.765 4 0.952 10 18O 1.68 2 1.8 1 30Si
0.82 1 0.62 1 48Ti 0.11 5 0.13 1 49Ti 0.24 2 0.23 1 50Ti 5.14 2
7.36 2 51V 1.61 1 1.31 2
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Table III: List of isotopes with the extracted spectroscopic
factors and other information such as the mass number (A), charge
number (Z) and neutron number (N) for the nuclei. jπ, T and Sn are
the spin and parity, isospin and neutron separation energy of the
nuclei. For completeness, we also list the root mean square radii
obtained from the calculations which yield the spectroscopic
factors as explained in the text. Endt’s compiled values are also
listed when available. Isotope A Z N jπ T S_n rms Endt SF LB-SM
Interaction
6Li 6 3 3 1+ 0 5.66 2.91 1.08 ± 0.305 0.684 PPN 7Li 7 3 4 3/2-
1/2 7.25 2.81 1.82 ± 0.257 0.628 PPN
8Li 8 3 5 2+ 1 2.03 3.66 0.61 ± 0.173 1.085 PPN 9Li 9 3 6 3/2-
3/2 4.06 3.23 0.98 ± 0.277 0.810 PPN
9Be 9 4 5 3/2- 1/2 1.67 3.86 0.44 ± 0.027 0.568 PPN 10Be 10 4 6
0+ 1 6.81 2.96 1.53 ± 0.153 2.356 PPN 11Be 11 4 7 1/2+ 3/2 0.50
7.11 0.52 ± 0.060 0.743 SPSDPF10B 10 5 5 3+ 0 8.44 2.85 0.49 ±
0.069 0.600 PPN 11B 11 5 6 3/2- 1/2 11.45 2.73 1.34 ± 0.134 1.094
PPN 12B 12 5 7 1+ 1 3.37 3.46 0.45 ± 0.064 0.826 PPN 12C 12 6 6 0+
0 18.72 2.53 2.98 ± 0.344 2.849 PPN 13C 13 6 7 1/2- 1/2 4.95 3.26
0.79 ± 0.038 0.613 PPN 14C 14 6 8 0+ 1 8.18 3.00 1.56 ± 0.127 1.734
PPN 15C 15 6 9 1/2+ 3/2 1.22 5.51 1.11 ± 0.314 0.980 SPSDPF14N 14 7
7 1+ 0 10.55 2.87 0.73 ± 0.084 0.692 PPN 15N 15 7 8 1/2- 1/2 10.83
2.89 1.38 ± 0.113 1.459 PPN 16N 16 7 9 2- 1 2.49 4.26 0.42 ± 0.119
0.960 SPSDPF16O 16 8 8 0+ 0 15.66 2.74 2.23 ± 0.149 2.000 PPN 17O
17 8 9 5/2+ 1/2 4.14 3.48 0.84 ± 0.045 1.000 SDPN 18O 18 8 10 0+ 1
8.04 3.24 1.75 ± 0.202 1.579 SDPN 19O 19 8 11 5/2+ 3/2 3.95 3.57
0.41 ± 0.058 0.685 SDPN 19F 19 9 10 1/2+ 1/2 10.43 2.66 1.56 ±
0.221 0.558 SDPN 20F 20 9 11 2+ 1 6.6 3.39 0.01 ± 0.003 0.019
SDPN
21Ne 21 10 11 3/2+ 1/2 6.76 3.41 0.01 0.03 ± 0.003 0.028 SD 22Ne
22 10 12 0+ 1 10.36 3.27 0.19 0.23 ± 0.033 0.013 SDPN 23Ne 23 10 13
5/2+ 3/2 5.2 3.58 0.24 0.24 ± 0.034 0.034 SDPN 24Na 24 11 13 4+ 1
8.87 3.49 0.3 0.56 ± 0.158 0.391 SDPN 24Mg 24 12 12 0+ 0 16.53 3.13
0.40 ± 0.057 0.221 SDPN 25Mg 25 12 13 5/2+ 1/2 7.33 3.50 0.37 0.29
± 0.029 0.343 SDPN 26Mg 26 12 14 0+ 1 11.09 3.35 1.8 2.79 ± 0.228
2.510 SDPN 27Mg 27 12 15 1/2+ 3/2 6.44 3.90 0.58 0.44 ± 0.124 0.464
SDPN 27Al 27 13 14 5/2+ 1/2 13.06 3.31 1.1 1.35 ± 0.191 1.101 SDPN
28Al 28 13 15 3+ 1 7.73 3.78 0.5 0.64 ± 0.091 0.602 SDPN 28Si 28 14
14 0+ 0 17.18 3.22 4.23 ± 1.196 3.618 SDPN
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29Si 29 14 15 1/2+ 1/2 8.47 3.73 0.55 0.37 ± 0.037 0.451 SDPN
30Si 30 14 16 0+ 1 10.61 2.87 0.89 0.72 ± 0.102 0.820 SDPN 31Si 31
14 17 3/2+ 3/2 6.59 3.70 0.75 0.59 ± 0.083 0.584 SDPN 32P 32 15 17
1+ 1 7.94 3.64 0.8 0.53 ± 0.075 0.601 SDPN 32S 32 16 16 0+ 0 15.04
3.40 1.46 ± 0.413 0.956 SDPN 33S 33 16 17 3/2+ 1/2 8.64 3.63 0.7
0.67 ± 0.190 0.609 SDPN 34S 34 16 18 0+ 1 11.42 3.53 1.9 1.38 ±
0.195 1.834 SDPN 35S 35 16 19 3/2+ 3/2 6.99 3.77 0.38 0.29 ± 0.082
0.364 SDPN 37S 37 16 21 7/2- 5/2 4.3 4.02 0.88 ± 0.124 35Cl 35 17
18 3/2+ 1/2 12.64 3.51 0.33 ± 0.093 0.318 SDPN 36Cl 36 17 19 2+ 1
8.58 3.70 1.2 0.69 ± 0.195 0.766 SDPN 37Cl 37 17 20 3/2+ 3/2 10.31
3.64 0.95 1.03 ± 0.146 1.152 SDPN 38Cl 38 17 21 2- 2 6.11 3.94 0.78
1.74 ± 0.492 36Ar 36 18 18 0+ 0 15.26 3.45 3.23 ± 0.457 2.055 SDPN
37Ar 37 18 19 3/2+ 1/2 8.79 3.71 0.49 0.35 ± 0.049 0.364 SDPN 38Ar
38 18 20 9+ 1 11.84 3.60 2.5 2.43 ± 0.687 3.043 SDPN 39Ar 39 18 21
7/2- 3/2 6.6 3.94 0.64 0.79 ± 0.112 40Ar 40 18 22 0+ 2 9.87 3.83
1.2 1.05 ± 0.297 41Ar 41 18 23 7/2- 5/2 6.1 4.01 0.47 0.55 ± 0.078
39K 39 19 20 3/2+ 1/2 13.08 3.58 2 2.1 ± 0.594 1.720 SDPN 40K 40 19
21 4- 1 7.8 3.90 0.94 1.66 ± 0.470 41K 41 19 22 3/2+ 3/2 10.1 3.84
0.56 0.95 ± 0.269 42K 42 19 23 2- 2 7.53 3.96 0.34 0.77 ± 0.109
40Ca 40 20 20 0+ 0 15.64 3.81 4.3 ± 0.385 4.000 SDPN 41Ca 41 20
21 7/2- 1/2 8.36 3.90 0.85 0.99 ± 0.055 1.000 FPPN 42Ca 42 20 22 0+
1 11.48 3.82 1.6 1.97 ± 0.176 1.810 FPPN 43Ca 43 20 23 7/2- 3/2
7.93 3.97 0.58 0.62 ± 0.072 0.750 FPPN 44Ca 44 20 24 0+ 2 11.13
3.87 3.1 4.37 ± 0.437 3.640 FPPN 45Ca 45 20 25 7/2- 5/2 7.41 4.03
0.39 ± 0.055 0.504 FPPN 47Ca 47 20 27 7/2- 7/2 7.28 4.08 0.25 ±
0.035 0.256 FPPN 48Ca 48 20 28 0+ 4 9.95 3.99 7.05 ± 0.814 7.383
FPPN 49Ca 49 20 29 3/2- 9/2 5.15 4.59 0.68 ± 0.068 0.918 FPPN 45Sc
45 21 24 7/2- 3/2 11.32 3.89 0.34 0.29 ± 0.082 0.352 FPPN 46Sc 46
21 25 4+ 2 8.76 4.00 0.49 ± 0.139 0.370 FPPN 46Ti 46 22 24 0+ 1
13.19 3.85 2.38 ± 0.337 2.580 FPPN 47Ti 47 22 25 5/2- 3/2 8.88 4.01
0.01 ± 0.003 48Ti 48 22 26 0+ 2 11.63 3.94 0.12 ± 0.012 49Ti 49 22
27 7/2- 5/2 8.14 4.08 0.23 ± 0.027 50Ti 50 22 28 0+ 3 10.94 4.00
6.25 ± 0.625 51Ti 51 22 29 3/2- 7/2 6.37 4.46 1.21 ± 0.342 51V 51
23 28 7/2- 5/2 11.05 4.01 1.49 ± 0.172
50Cr 50 24 26 0+ 1 13 3.94 0.11 ± 0.031 51Cr 51 24 27 7/2- 3/2
9.26 4.08 0.27 ± 0.038
-
52Cr 52 24 28 0+ 2 12.04 4.00 6.03 ± 0.853 53Cr 53 24 29 3/2-
5/2 7.94 4.34 0.38 ± 0.025 55Cr 55 24 31 3/2- 7 /2 6.24 4.03 0.86 ±
0.243
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Figure 1: (Color online) Comparison of digitized data (open
points) and tabulated data (closed points) from the same
measurement of the angular distributions of the protons obtained in
the 14N(d,p)15N reaction at incident deuteron energy of 12 MeV. The
curve is the predicted angular distributions from the code TWOFNR
as described in the text, multiplied by 1.1 which is the
spectroscopic factor. Ref. [21]
Ref. [82]
-
Figure 2: (Color online) The angular distributions of the
deuteron obtained in the 44Ca(p,d) 43Ca reaction at incident proton
energy of 40 MeV [174]. The curve is the predicted angular
distributions from the code TWOFNR as described in the text,
multiplied by the spectroscopic factor.
Ref. [175]
-
Figure 3: (Color online) Comparisons of the angular
distributions of the deuteron measured in the 11B(d,p)12B reactions
in three different experiments.
Ref. [45]
Ref. [21]
Ref. [46]
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Figure 4: (Color online) Comparisons of the angular
distributions of the deuteron measured in the 12C(d,p)13C reactions
in four different experiments. Ref. [45]
Ref. [21]
Ref. [30]
Ref. [59]
-
Figure 5: (Color online) Comparison of spectroscopic factors
obtained from Ref. [181] (open circles) and from other measurements
(closed circles). The increase of spectroscopic factors observed at
Ed
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Figure 6: (Color online) Angular distributions for 40Ca(d,p)41Ca
reactions for beam energy from 4.69 to 56 MeV. Each distribution is
displaced by factors of 10 from adjacent distributions. The overall
normalization factor is 10 for the 7.2 MeV data. References are
listed in Table 1.
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Figure 7: (Color online) Comparisons of the angular
distributions of the deuteron measured in the 50Cr(p,d)49Cr
reactions in four different experiments.
-
Figure 8: (Color online) Comparisons of three angular
distributions of the deuteron measured in the 14C(d,p)15C reactions
in three different experiments. The curve is the predicted angular
distributions from the code TWOFNR as described in the text,
multiplied by the spectroscopic factor of 1.1 which fits the data
of ref. [74], the only set of data with measurements at angles more
forward than 15°. Ref. [74]
Ref. [71]
Ref. [75]
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Figure 9: (Color online) Comparisons of spectroscopic factors
obtained from (p,d) and (d,p) reactions as listed in Table II. The
line indicates perfect agreement between the two values.
-
Figure 10: (Color online) Comparisons of spectroscopic factors
obtained from this work and the compiled values of Endt [8]. All
the values are listed in Table III. The line indicates perfect
agreement between our values and Endt’s compilation.
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Figure 11: (Color online) Ratios of the SF values from
experiment divided by the SF values predicted by the large basis
shell model as a function of the neutron separation energy (Sn).
Open and closed symbols denote elements with odd and even Z
respectively. The three different colors of green, blue and red
represent Z=3-8, 9-18 and 19-22 isotopes respectively.
Abstract II. Reaction model III Compilation and digitization of
angular distribution data IV. Extraction of spectroscopic factors
V. Evaluation of the angular distribution measurements VI. Transfer
reactions at high and low energy VII. Nuclei with small
spectroscopic factors VIII. Comparison of Spectroscopic factors
obtained from (p,d) and (d,p) reactions IX. Comparison with Endt’s
“best values” XI. Dependence of spectroscopic factors on neutron
separation energy XII. Summary References